Evaluation metrics in ML

1. Confusion matrix - A confusion matrix is an $N\times N$ matrix, where $N$ is the number of predicted classes. It is extremely useful for measuring precision-recall, Specificity, Accuracy, and most importantly, AUC-ROC curve.
   Type 1 Error = $FP$
   Type 2 Error = $FN$

2. Accuracy - Fraction of correct predictions made by the model over the total number of predictions $$Accuracy=\frac{TP+TN}{TP+TN+FP+TN}$$
3. Precision - The ratio of correctly predicted positive observations to the total predicted positives. It is useful when the cost of false positives is high. $$Precision=\frac{TP}{TP+FP}$$
4. Recall (Sensitivity or True Positive Rate) - measures the fraction of true positive predictions out of the total number of actual positive instances. It is useful when the cost of false negatives is high. $$Recall=\frac{TP}{TP+FN}$$
5. F1 score - harmonic mean of precision and recall, providing a single metric that balances both measures. It is often used in cases where both precision and recall are important. \ $$F1=\frac{2\times (Rrecision\times Recall)}{(Precision+Recall)}$$
6. ROC - AUC (Receiver Operating Characteristic - Area Under Curve) The ROC curve is plotted with TPR vs. FPR at various threshold settings, and the AUC represents the likelihood that the model ranks a random positive instance higher than a random negative instance. The AUC-ROC represents the probability that the model will rank a random positive instance higher than a random negative instance.
7. Regression metrics

8. $R2$ $score=\frac{1-S{S}_r}{S{S}_m}$